|Joint IAS/Princeton University Number Theory Seminar|
|Topic:||Decoupling in harmonic analysis and the Vinogradov mean value theorem|
|Affiliation:||IBM von Neumann Professor; School of Mathematics|
|Date:||Thursday, December 17|
|Time/Room:||5:30pm - 6:30pm/S-101|
Based on a new decoupling inequality for curves in $\mathbb R^d$, we obtain the essentially optimal form of Vinogradov's mean value theorem in all dimensions (the case $d = 3$ is due to T. Wooley). Various consequences will be mentioned and we will also indicate the main elements in the proof (joint work with C. Demeter and L. Guth).